Probability Calculator

N

K

n

k1

k2

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I promise, it's easy! Examples ahead, just keep reading.The Hypergeometric Distribution Function is a big, bad and yet useful mathematical monster that really helps to calculate probabilities applied to card games. It assumes there are "good draws" (called successes) and "bad draws" and it accounts for sampling without replacement, that is a formal way to say you draw cards from a deck (the population) into your hand (the sample) and you don't put them back into it, so it's well suited for card games. Here's a description of the parameters above.

N

Population size => total cards into your deck

K

Successes in that population => cards considered "successes" into your deck

(Minimum) successes wanted into the drawn cards, must be <= K for obvious reasons: you can't draw the fifth Elvish Priest if you've got just 4x into your deck!

k2

Maximum successes into the drawn cards, like for k1 it must be <=K for the same reason AND it must be >= k1. If it's set, it cumulates all the probabilities from k1 to k2 (see examples), else if k2 = 0 or empty or <= k1 the value of k1 is used as a fallback. You can usually read it as "at least k1 copies and no more than k2 copies"

Examples Click buttons to calculate

{N:40, K:4, n:5, k1:1, k2:4}
You have 40 cards into your deck with a 4x of a powerful cost 1 you want to see on the opening hand, so you put the values above and you get 42.71% chance of this happening. Not bad, but it's less than 50% so it's more likely NOT to happen. Try it for yourself clicking the button on the left or putting the values yourself then hit "Calculate!"

{N:40, K:4, n:10, k1:1, k2:4}
Same situation as above, but you desperately want that cost 1 card on the opening hand, so you mulligan hard all the 5 cards you drew and try it again. To simulate mulligan, put n = 10 (draw 5, then draw another 5). Now gives a whopping 70.01%, much more likely than the previous 42.71%!

{N:40, K:8, n:10, k1:1, k2:10}
You have 4x Ruler's Memoria into your Magic Stone Deck and your're running 8 of any cost 0 Regalia cards into your 40 cards Main Deck. You want to know what are the odds of getting at least a regalia. You get a nice 92.39%.Twist: to actually calculate what are the odds of not getting the regalia AND getting a rested Ruler's Memoria at the same time on turn 1, a player's nightmare, you have to get the opposite probability of the previous value, so P = 100% - 92.39% = 7.61% of NOT getting a regalia and then multiply it by the chance of getting the memoria (that is 40%, given by {N:10, K:4, n:1, k1:4, k2:0}), so P = 7.61% * 40% = 3.04%, pretty unlikely. Pfiuu!

{N:10, K:4, n:4, k1:1, k2:4}
Now the stones! Assume you play 10 Magic Stones of which 4x Black Moon's Memoria and 6x Magic Stone of Darkness, you're sure you'll have "Call of the Primogenitor" in hand by the turn 3 to play it and you call 1 stone per turn. What are the chances of playing that card with its [Awakening] cost with that Magic Stone Deck? Your "success" cards are the 4x Black Moon's Memoria and you have to calculate the chance of getting at least 1x Black Moon's Memoria by turn 3 (3 stones drawn on the board). So you put {N:10, K:4, n:4, k1:1, k2:4} where k1 and k2 can be read as "at least k1 and no more than k2" Black Moon's Memoria. You get 92.86%, so you'll likely be able to play that [Awakening] assuming you have the Call into your hand.

{N:60, K:4, n:7, k1:1, k2:4}
Remember example 1? Let's compare it with Magic: The Gathering, assuming a 60 cards deck with a precious 4x you want to see on the opening hand, no mulligan. You get 39.95%, pretty close to the 42.71% we got earlier.